This is not a new question here and here, but the details make it differ.
My input log file looks like:
TEMP MON -=- Sat Aug 15 02:20:24 EEST 2020 -=-
You may use this awk solution:
awk 'BEGIN {
FS=OFS=" -=- "
}
{
cmd = sprintf("TZ=EET date -d \"%s\" +\"%Y-%m-%%d_%T %Z\"", $2);
if ((cmd | getline output) > 0)
$2 = output
close(cmd)
} 1' file
TEMP MON -=- 2020-08-15_02:20:24 EEST -=- 48.6
TEMP MON -=- 2020-08-15_02:20:50 EEST -=- 49.1
TEMP MON -=- 2020-08-15_02:21:13 EEST -=- 49.1
TEMP MON -=- 2020-08-15_02:21:44 EEST -=- 49.1
TEMP MON -=- 2020-08-15_02:21:45 EEST -=- 48.6
TEMP MON -=- 2020-08-15_02:21:52 EEST -=- 49.1
TEMP MON -=- 2020-08-15_02:21:53 EEST -=- 48.6
TEMP MON -=- 2020-08-15_02:21:54 EEST -=- 49.6
TEMP MON -=- 2020-08-15_02:21:56 EEST -=- 49.1
TEMP MON -=- 2020-08-15_02:21:57 EEST -=- 49.1